Question

Show that if two metrics induce the same topology, one metric space is compact iff the other one is.

score 352 · Answer 1 · 2026-04-15 04:13:53

352

Views

Show that if two metrics induce the same topology, one metric space is compact iff the other one is.

Published on 15 Apr 2026 - 4:13

score 97 · Answer 2 · 2026-04-17 13:36:50

97

Views

choose the correct option regarding complete metric space

Published on 17 Apr 2026 - 13:36

score 183 · Answer 3 · 2026-04-15 05:37:09

183

Views

Proving $B=\{f:f\in C_{[0,1]}\text{ and }\:d(f,0)\leqslant 1\}$ is not compact

Published on 15 Apr 2026 - 5:37

score 44 · Answer 4 · 2026-04-11 10:49:46

44

Views

Continuous paths and limits of linear interpolations

Published on 11 Apr 2026 - 10:49

score 356 · Answer 5 · 2026-04-11 12:32:15

356

Views

What is the precise definition of a multi-connected manifold?

Published on 11 Apr 2026 - 12:32

score 313 · Answer 6 · 2026-04-13 04:10:45

313

Views

Inverse Limit of Dense Subsets is Dense

Published on 13 Apr 2026 - 4:10

score 128 · Answer 7 · 2026-04-13 06:49:31

128

Views

Contradiction in the proof a space with every compact subspace is not Hausdorff

Published on 13 Apr 2026 - 6:49

score 201 · Answer 8 · 2026-04-14 11:32:39

201

Views

Nearest point property and uniformly continuous image

Published on 14 Apr 2026 - 11:32

score 44 · Answer 9 · 2026-04-09 20:03:39

44

Views

What are the connected components of the real general linear group?

Published on 09 Apr 2026 - 20:03

score 423 · Answer 10 · 2026-04-16 06:29:19

423

Views

Quotient map between homotopy equivalent spaces

Published on 16 Apr 2026 - 6:29

score 467 · Answer 11 · 2026-04-16 00:10:43

467

Views

Equivalent condition for normal topological space

Published on 16 Apr 2026 - 0:10

score 152 · Answer 12 · 2026-04-13 16:18:18

152

Views

Lipschitz function and incomplete range

Published on 13 Apr 2026 - 16:18

score 83 · Answer 13 · 2026-04-11 11:04:39

83

Views

Locally compact allows shrinking compact neighborhood without hausdorff property?

Published on 11 Apr 2026 - 11:04

score 195 · Answer 14 · 2026-04-29 12:25:52

195

Views

Does a continuous function preserve metrizability?

Published on 29 Apr 2026 - 12:25

score 142 · Answer 15 · 2026-04-09 20:44:25

142

Views

More on flimsy spaces

Published on 09 Apr 2026 - 20:44

List Question

Show that if two metrics induce the same topology, one metric space is compact iff the other one is.

choose the correct option regarding complete metric space

Proving $B=\{f:f\in C_{[0,1]}\text{ and }\:d(f,0)\leqslant 1\}$ is not compact

Continuous paths and limits of linear interpolations

What is the precise definition of a multi-connected manifold?

Inverse Limit of Dense Subsets is Dense

Contradiction in the proof a space with every compact subspace is not Hausdorff

Nearest point property and uniformly continuous image

What are the connected components of the real general linear group?

Quotient map between homotopy equivalent spaces

Equivalent condition for normal topological space

Lipschitz function and incomplete range

Locally compact allows shrinking compact neighborhood without hausdorff property?

Does a continuous function preserve metrizability?

More on flimsy spaces

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